Field of the Invention
This application relates to statistical shape models. More particularly, this application relates to establishing correspondence between training shapes when constructing a statistical shape model.
Description of the Related Technology
Statistical models of shape have been used for some time to provide automated interpretation of images. The basic idea used by the models is to establish, from a training set, a pattern of “legal” variation in the shapes and spatial relationships of structures in a given class of images (the class of images may be for example face images, hand images, etc.). Statistical analysis is used to give an efficient parameterization of the pattern of legal variation, providing a compact representation of shape. The statistical analysis also provides shape constraints which are used to determine whether the shape of a structure in an analyzed image is a plausible example of the object class of interest.
One aspect of developing a statistical shape model is to establish, during training, dense correspondence between shape boundaries for a reasonably large set of example images. It is important to establish the “correct” correspondence, i.e., a landmark should represent the same location for each of the images used to generate the model (for example a landmark could be located at the inner corner of the left eye). If “correct” correspondences are not established, an inefficient model of shape can result, leading to difficulty in defining shape constraints. In other words, the model will not correctly determine whether the shape of a hypothetical structure in an analyzed image represents a plausible example of the object class of interest.
The problem of establishing correspondence can be viewed as one of finding an appropriate parameterization of the shape. The term parameterization refers to the process of defining a one-to-one correspondence between values of one or more parameters and position on the shape so that a given value of the parameter (or parameters) defines a unique location on the shape. For example, a single parameter can define position around a closed boundary, while two parameters are required to define position on a closed surface (in 3D) of spherical topology.
In practice, correspondence has been established for training images by using manually defined “landmarks”. In 2D this defines a piecewise linear parameterization of each shape, with equivalent landmarks for the different shapes corresponding by definition and intermediate sections of shape boundary parameterized as a linear function of path length. Shape models generated in this way have been found to function reasonably well.